Mathematicians. I googled this word and came across a list titles “The 100 greatest Mathematicians of the Past.” The list includes names like Archimedes, Guass, Euler, and Reimann, all names that are often studied and have many concepts names after them. These mathematicians, and others, have made big contributes to the math world and have helped others increase their understanding in different topics. As I continues to look for other pages that talked about mathematicians, I came across a Wikipedia definition that reads, “A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.” Using this definition, it is clear that the list of 100 mathematicians are all mathematicians. But there are many mathematicians in the world that are not on the list. When looking at mathematics in the past, men were the only ones who could get the recognition for their ideas and many times their ideas did not get recognized until they were older.
Even today gender and age can influence what culture says a mathematician is. But I want to challenge that. As a female studying mathematics I see firsthand that mathematicians are everywhere. I see many females in my course that solve many problems and have a deep understanding of many different mathematical concepts. There are female professors that have shaped my view of mathematics and who I would also consider mathematicians. We even studied females who have made contributions to the math world. But not only am I mathematics major, but I am an elementary education major. In many ways I see the children that I get to work with as mathematicians. They are working on problems and using many different strategies to solve the question in front of them. Their knowledge of math is big, and it is growing with every passing day and their work is their studying. We are starting to break the stereotypes of mathematics by just naming more and more people as mathematics.
Calling all my students mathematicians is something that I want to take into my classroom in the near future, but that is not the only thing I want them defined as. Each student is unique with different gifts that I want celebrated and different talents I want to be encouraged. There are some students who will understand mathematic ideas quicker and others who will grasp language, science, or social study standards easier. I want my students to be mathematician, scientists, and historians. But more importantly I want them to be them, just full of confidence in the subjects that they are learning.
A little over four years ago I declared math as the first of my two majors, the second being education (with a minor in elementary education). But when people out side of the math department asked me what I was studying I would often just say education. When ask what my major focus was, I would honestly say math, bracing myself for the reactions that would come. I was not prepared to answer the question Why Math?
This semester I am finishing my mathematics major and reflecting on why I choose math and why I stuck with it for these last four years. It was not because it was easy or because I enjoyed every moment of it, but because I learned and I grew.
ITS BIGGER THAN THE NUMBERS. When the word math is thrown out, most people think of equations, shapes, numbers, and old frustrations. But in many of my math classes I gained insight as to what else math is. Often we were given tasks to solve and had to figure out the strategies that we could use to problem solve. Problem solving can be found in all levels of mathematics, and it gives students endurance and strategy to solve problems out side of their math classes. In other classes we had to communicate our work in a way that was clear and precise through writings, projects, or reflections. Communicating work clearly and precisely is a desirable skill in many settings, both professional and causal.
IT IS EVERYWHERE Many structures, paintings, flowers, and even bodies show characteristics of the golden ratio. This ratio is approximately equal to 1.61803 and has the Fibonacci numbers in every part of it. But even simpler than that, figuring out a tip after eating dinner out or getting a haircut can easily be done with out pulling out the calculator on the nearest smart phone. Seeing patterns in different designs while looking at art, floor tiles, or even a deck of cards. In almost everything we see and do, we can pull elements of mathematical practice from it.
IT HELPS ME UNDERSTAND EDUCATION Education was always my goal and math was just a long for the ride. But what surprised me most about so many of my math classes was that I got to understand student thinking so much better through those classes. Ideas like fixed and growth mindsets became more concrete because I was able see examples of both in those classes. I learned patience, determination, and that failure is not the end but the beginning. Education can be an intimidating field to enter because it is other people's lives you are affecting. But these math ideas are ideas I want to hold on to during my next step as I switch my roles in the classroom.
Sudoku. Logic. Magic Square. Tangram. Bridges.
Puzzles, like the ones listed above, often give people of any age problems that expand their mathematical thinking in a fun and creative way. This type of thinking always looks to see the effect that a move will have and understands that it is okay to mess up and learn from it. Puzzles are often created in many different levels so that they are accessible to a wide variety of people. I have seen puzzles completed in the Sunday newspaper and in a 3rd grade classroom. Puzzles keep the brain working. So why don't more people do puzzles, why aren't puzzles incorporated into education?
I have always enjoyed doing puzzles, but I know that not everyone enjoys them as much as I do. Often they cause people to get aggravated or annoyed if they mess something up or they are struggling to figure out the solution. However, I see this behavior and mindset among adults more than children. Mindset is a large focus when looking at education practices and the difference between and fixed mindset and a growth mindset is a topic that is being explored in a variety of ways. I believe puzzles can give students the chance to expand their thinking and learn how to work through a difficult task, leading them to a growth mindset. This growth mindset that can come from doing fun puzzles in the classroom setting will then be able to carry over into different mathematical ideas and even into other subjects.
Another benefit to incorporating puzzles into classroom work is that they start to see patterns and relationships between different sequences and numbers. Their mathematical thinking is heighten without the students even thinking they are doing math. The 8 standards for mathematical practice can be seen and even assessed in different puzzles. The following just some of the standards that basic puzzles will incorporate:
In class we had the chance to create a puzzle and it was something that made us think deeper and be creative. This use of puzzles in a college classroom is something that I would want to take into my own classroom. Having students create their own puzzles expands on their mathematical thinking and it causes them to look at the construction of a puzzle and use math to complete it. Creating something or being involved in the creation process will give students even more interest in their work because they feel a sense of control and passion for their work. They will want to test their classmates and see if they could solve each other's puzzles. Their thinking would be deep and useful.
Puzzles are fun and so helpful when looking at education and even beyond, If we give students the tools and techniques to solve puzzles, just think about the puzzles they will be able to solve down the road with the dedication and strategy they learned while having fun.
Some links with puzzles for kids of all ages!
What initially drew me to this book was how Eugenia Cheng relates many day-to-day concepts, such as baking, to the large world of mathematics. Well reading, this idea remained while I read and I gained a lot of other knowledge was well. The mathematical ideas found in this book are vast, the connections to teaching, especially in an elementary setting are few, but profound, and math concepts can be found in many different settings and practices. I would recommend this book for the amount of information that Cheng discusses, and how clearly she presents it.
Cheng presents many mathematical ideas, but clearly states them all. I often found myself going back to previous math classes, wishing I had her explanation on topics that I struggled with. Not only did she present the ideas clearly, but she also gave well thought out examples that reinforced the ideas.
The book was an easy read, but I often found myself wanted to stop reading so that I could sit with an idea before we jumped to the next one on the following page. I would recommend this book, but would also recommend that the reader take their time working through it and enjoy the connections that Cheng puts in the text. I believe that Cheng wants readers to enjoy math and enjoy the process and details of math, similar to enjoying baking and the many details that go in to it. Go get a piece of pie and grab the book and enjoy.
Al-Khwarizmi is a name that I was not familiar with, but the work we did in class about him intrigued me. But before we get too far, it is important to know a little background on Al-Khwarizmi. He was a part of the Islamic Golden Age, which was a time that many scientific and mathematical works took off. In fact, he was even one of the first directors of the House of Wisdom in Baghdad. He also wrote a book, but this book was not a love story or picture book, it was The Compendious Book on Calculations by Completion and Balancing. He wrote a math book. It contained a lot of information about numbers and algebra as he knew it, some he gathers and others he may have created. The crazy thing is, he never thought of negative numbers while writing the book. But that is not the part that I found most interesting, it was the way that they solved different equations verbally.
In class, we were given time to read through the solution to the problem "a square and ten roots are equal to 39 Dir-hems". Just reading that I had no idea where to start, so I kept reading and it became more and more confusing to me. He was telling us step by step of what to do, but I was not used to the terms that were used or the only verbal solution. After we broke it down in groups and as a class it made sense and it was so neat to see the connections!
This mathematician and problem got me thinking more as a role of a teacher too. I struggled to see how to solve this problem because it was all new to me. I did not understand the language and it was set up in a way that was unfamiliar to me. To solve and follow the problem I needed more information. Often math can be a subject that seems foreign to students and the symbols or way it is written doesn't make sense. As a teacher, I will want my students to struggle with problems so that they can learn, but I also want to give them the tools that they need to learn and understand what the problem is asking. Also, I started to think more about the how math is shown with visuals and symbols and how helpful that is for students to see the problem and solution more than hearing it.
Math. Math can be numbers and calculations with those numbers. Math can be equations and graphs and tables. Math can be problem solving and critical thinking. Math can be patterns and sequences. Math can be shapes and angles. Math can be logic. And I think that math is all of these things and more. When we look around, we can see math in almost everything that we do and experience. When we wake up to an alarm and push snooze 3 times, each time giving an 10 extra minutes of sleep, you do math to figure out how much extra sleep you got. Looking at the ripples after you toss a stone into the lake, you can find a mathematical pattern to describe the event. A few years ago, my view on math was finite, I saw it mainly as numbers and doing things with them. But I have been learning that math is more about the process than the final answer. There is beauty in growing your mind and problem solving by using what you do know rather than focusing on what you do not know. Math is infinite.
Math has a history and everything that is discovered now, wasn't always discovered. I feel that five pretty important milestones in the mathematical world are the following:
2. Pythagorean Theorem
3. Euclid's Postulates
4. Area & Volume Equations
These 5, along with many other discoveries play an important role in mathematics today. They are used by mathematicians of all ages and used in basic and complex ways.